There are so many fun ways to explore what angles are. I want my children to be fluent with angles. Learning is not about memorizing something to pass a test, it is about understanding the language and patterns of different things. It is about developing fluency. Here are a few of the many activities for learning about angles I found helpful with my children.
The Jumping Angle Game
The first part of the Angle Game is making the game board. The game board should be a circle divided into twelve equal parts. Each player also needs twelve markers of one color and one of another color. Finally you need a set of playing cards with numbers 1 – 10 on them (four of each number). Each player gets to place his uniquely colored game piece on the outer edge of one of the lines.
Then players take turns drawing cards. The number on the card signifies how many 1/12ths of the board the person moves. So if you draw a 3, you move to the third line away from where you were, leaving one of the twelve markers on the line he or she moved away from. The player gets to choose the direction his or herself and should name the angle formed by the lines he or she is leaving and the one he or she is moving to. In the case of 3, the angle would be 90 or a square angle. Beginners can use the names acute, right, obtuse, straight or reflex. Older players can name the number of degrees.
The goal of the game is to have landed on every line and the twelve colored markers left on the lines keep track of which lines you have yet to visit. Since you never know what number you are going to draw next, the game is based entirely on luck. A variation of the game could probably be played where players hold four card numbers in his or her hands and choose which number to play at which point, thus giving a person more control and requiring more planning. I had allowed the choice of direction because I know my son enjoys games more if he has a choice to make but if you play it where you get to choose which of several cards to play, then you wouldn’t need to have the option of direction. Red suits could signify negative angles and black suits positive angles.
Since the player can choose which direction to move, a card for 3 is equivalent to the card for 9, since moving 90 degrees one direction is the same as moving 270 degrees the other direction. The same is true for most of the other cards. So for most distances there are two cards that could be drawn that would get you there. Only the 30 degree jump and 180 degree jumps are not duplicated. The 180 degree jump can be done only with the six card. The 30 degree jump can be done only with one, since there is no card for 11.
I invented this game for my son because I wanted him to have extra practice and experience with the angles. I think it is a good thing to be able to estimate that 240 degrees is under three quarters of the way around a circle. An extra bonus was that it encouraged my son to practice multiplying by 30 to find which degree jump he could make. He also noticed that whichever line he was on became a line of symmetry and when he was deciding which direction around the circle to go he could count out one distance and look for the mirror image of it.
Another variation of the game that would be really fun would be to make out a really big circle on the floor, have the children be their own game piece with the goal of “planting” beans at each of the lines.
One of the joys of homeschooling is I get to go back now and study all the things I wanted to as a child but didn’t know how to. One of those things is astrolabes. My children aren’t quite up to learning how to calculate the latitude with them yet, but we still can explore how to measure angles. I made an easy Astrolabe out of card paper, string and tape
. (Based roughly off the description linked too, but I used a tube of cardpaper instead of a drinking straw since my children found a drinking straw to hard to look through.)
I set them about measuring the house. I had them stand first at the bottom of the stairs and measure the angle to a picture hook at the top of the stairs. We talked about why the angle was different for each of us (because we were looking at it from different heights). We drew out a little diagram to explain why the angles were different. I had them predict the if the angle would be smaller or larger if we moved in different places or if one person measured than another.
I made a second astrolabe based off of the mariners astrolabe, which we used to measure the angle of different points of the room to the lightbulb, aligning the shadow cast.
Snowflakes and Pop-up Cards
Remember those paper snowflakes you make by folding a circle of paper and then cutting triangles around the edges? Well those are a perfect chance to explore angles. If you fold the paper so that you can see a 90 degree slice of it, how many layers of paper do you have? If you fold the paper so you see a 60 degree slice, how many do you have? If you cut two lines in to the triangle that meet at an acute angle but unfold into a diamond, what type of angle will the other two angles of the diamond be?
Paper pop-up cards also work on angles. When they are closed, what angles are they? Bend one open slowly, slowly, slowly and pause to peek from the side at what angle the pop-up part is. Where it juts off of the main card, is it obtuse? What angle are the sides of the cards to each other? Acute? Open the card really wide. Now what angle are the parts where the pop-up part juts away from the card? Talk about how the total angle is always 360.
Making Right Angles
There are lots of different ways to figure out how to make a right angle. The ancient Egyptians made right angles using a string with 12 equally spaced knots. By pulling specific knots apart they could form a right angle triangle. Can you figure out which knots would be pulled? What other angles can the same method create?
The program Math in a Cultural Context
talks about the way one Yup’ik elder made right angles from hides. She would fold the hide once one direction so she had a straight edge and then fold the hide the other direction so that the two parts of the straight edge matched up. Then she knew it was a right angle.